United Airlines - 2 guns max per hardcase?

I'm flying United pretty soon, and was planning on taking 2 handguns and a shotgun in a locked, hardsided case. United's website has a section under "baggage" for firearms, but it just links you to the TSA regs.

I called United, and finally got through to their call center in India. The guy told me that he thought United had a two "shotgun" (firearm?) per hardcase maximum.

Is this correct? And if so, isn't this a more stringent requirement than TSA imposes? If this is in fact the TSA-imposed maximum number of firearms per hardcase, could someone kindly point me to those regulations?

Handguns can be put in a suitcase if you are taking one along. Actually, handguns can fit and go in any baggage you are checking in (as opposed to bags carried on). You just have to declare them, pack them as prescribed (unloaded, separate from the ammo, etc), and do what they tell you to do at check in. Not a big deal. They do not have to be put in a gun-specific bag or case.

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